(Also, a "dirty little secret" that I stumbled on as a kid and that helped me stay at the top of my class for a long, long time without ever having to make much of an effort: you can usually check your results by keeping an eye on "extra-mathematical" aspects; for instance the answer to one exercise will follow the same pattern as the answers to all the other exercises; if you've been getting round numbers, then the right answer is probably also a round number; unless maybe it's the last exercise in the set, the one that gives the top student the extra point. If it's a trig exercise, the right answer is probably a multiple of 15 or even 30 degrees. These "facts" make no sense in terms of actual math; and it's even possible that learning them was harmful for me and one of the things that curtailed my later math learning. But for a while they made for smooth sailing.)

I think the short term for this is metagaming. :)